Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 37
... INTERIOR ANGLES ON THE SAME SIDE , are those that lie on the same side of the secant and within the other two lines . Thus , BGH and GHD are interior angles on the same side . 2o . EXTERIOR ANGLES ON THE SAME SIDE are those BOOK I. 37.
... INTERIOR ANGLES ON THE SAME SIDE , are those that lie on the same side of the secant and within the other two lines . Thus , BGH and GHD are interior angles on the same side . 2o . EXTERIOR ANGLES ON THE SAME SIDE are those BOOK I. 37.
Page 38
... angles . Thus , AGH H B 4 ° . ALTERNATE EXTERIOR ANGLES are those that lie on opposite sides of the secant and without the other two lines . Thus , AGE and FHD are alternate exterior angles . 5 ° . OPPOSITE EXTERIOR AND INTERIOR ANGLES ...
... angles . Thus , AGH H B 4 ° . ALTERNATE EXTERIOR ANGLES are those that lie on opposite sides of the secant and without the other two lines . Thus , AGE and FHD are alternate exterior angles . 5 ° . OPPOSITE EXTERIOR AND INTERIOR ANGLES ...
Page 39
... angles ( P. I. ) ; the sum of the angles FAG and GBD is equal to two right angles , by hypothesis : hence ( A. 1 ) ... interior angles equal , the two straight lines are parallel . Let the angles EGB and GHD be equal : Now EGB and AGH are ...
... angles ( P. I. ) ; the sum of the angles FAG and GBD is equal to two right angles , by hypothesis : hence ( A. 1 ) ... interior angles equal , the two straight lines are parallel . Let the angles EGB and GHD be equal : Now EGB and AGH are ...
Page 40
... interior angles on the same side is equal to two right angles . Let the parallels AB , CD , be cut by the secant line FE : then the sum of HGB and GHD is equal to two right angles . For , if the sum of HGB and GHD is not equal to two ...
... interior angles on the same side is equal to two right angles . Let the parallels AB , CD , be cut by the secant line FE : then the sum of HGB and GHD is equal to two right angles . For , if the sum of HGB and GHD is not equal to two ...
Page 41
... exterior and interior angles are equal . The angles DHG and HGA are equal , from what has just been shown . The angles HGA and BGE are equal , because they are ver- tical : hence , DHG and BGE are equal . In like manner , it may be ...
... exterior and interior angles are equal . The angles DHG and HGA are equal , from what has just been shown . The angles HGA and BGE are equal , because they are ver- tical : hence , DHG and BGE are equal . In like manner , it may be ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence